Signals, system, method and apparatus

ABSTRACT

Embodiments of the present invention provide a method to produce a modulation signal comprising combining at least two modulation signals, for example, BOCs or derivatives thereof, having portions (chip or a number of chips) thereof with respective relative phases or states ({++,−−} and {+−,−+}) selected such that the average of a plurality of said portions at least reduces cross spectral terms of the composite complex spectrum of said at least two modulation signals.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.12/305,401 filed on Apr. 1, 2009, entitled “Signals, System, Method andApparatus,” allowed, which is the U.S. national phase of InternationalApplication No. PCT/GB2007/002293 filed on Jun. 20, 2007 and publishedin English on Dec. 27, 2007 as International Publication No. WO2007/148081 A1, which application claims priority to Great BritainApplication No. 0612142.0 filed on Jun. 20, 2006, the entire contents ofall of which are incorporated herein by reference.

BACKGROUND TO THE INVENTION

Embodiments of the invention relate to signals, systems and methods suchas, for example, modulation, navigation and positioning signals, systemsmethods and receivers adapted to receive and process the same.

Satellite Positioning Systems (SPS) rely on the passive measurement ofranging signals broadcast by a number of satellites, or ground-based orairborne equivalents, in a specific constellation or group ofconstellations. An on-board clock is used to generate a regular andusually continual series of events, often known as ‘epochs’, whose timeof occurrence is coded into, or at least associated with, a random orpseudo-random code (known as a spreading code). As a consequence of thepseudo-random or random features of the time epoch encoding sequence,the spectrum of the output signal is spread over a frequency rangedetermined by a number of factors including the rate of change of thespreading code elements and the waveform used for the spreading signal.In the prior art, the spreading waveform is rectangular, of constantchipping rate, and has a (sinc)² function power spectrum, prior tofiltering by transmission circuitry.

The ranging signals are modulated onto a carrier signal for transmissionto passive receivers. Applications are known that cover land, airborne,marine and space use. Typically, binary phase shift keying is employedto modulate the carrier signal, which, itself, has a constant magnitude.Usually, at least two such signals are modulated onto the same carrierin phase quadrature. The resulting carrier signal retains its constantenvelope but has four phase states depending upon the two independentinput signals. However, it will be appreciated that the two modulatingsignals do not need to have the same carrier magnitude. It is possiblefor a constant carrier magnitude of the combined signal to be maintainedby appropriate selection of corresponding phases other than π/2 radians.

Techniques are known by which more than two signals are modulated ontothe same carrier using either additive methods (known as ‘Interplex’modulation) or a combination of angle modulation and additive methods,known as ‘Coherent Adaptive Sub-carrier Modulation’ (CASM). Both ofthese techniques require the addition of a further inter-modulationcomponent that is derived to maintain constant carrier magnitude. Forexample, in ‘Interplex’ modulation, techniques are known with threetransmitted components, 2 on one carrier phase with a third on thequadrature phase. These have at least six phase states.

An example of such a satellite positioning system is the GlobalPositioning System (GPS). Generally, the GPS operates using a number offrequencies such as, for example, L1, L2 and L5, which are centred at1575.42 MHz, 1227.6 MHz and 1176.45 MHz respectively. Each of thesesignals is modulated by respective spreading signals. As will beappreciated by those skilled in the art, a Coarse Acquisition (CA) codesignal emitted by the GPS Satellite Navigation System is broadcast onthe L1 frequency of 1575.42 MHz with a spreading code rate (chip rate)of 1.023 MHz. The CA code signal has a rectangular spreading waveform,is binary phase shift keyed on to the carrier, and is categorised asBPSK-R1. The GPS signal structure is such that the signal broadcast bythe satellites on the L1 frequency has a second component in phasequadrature, which is known as the precision code (P(Y) code) and madeavailable to authorised users only. The P(Y) signal is BPSK modulatedwith a spreading code at 10.23 MHz with a magnitude that is 3 dB lowerin signal power than the CA code transmission. Consequently, the Qcomponent has a magnitude that is 0.7071 (−3 dB) of the magnitude of theI component. It will be appreciated by those skilled in the art that thephase angles of these states of these signals are ±35.265° in relationto the ±1 axis (phase of the CA code signal as specified in ICD GPS200C). One skilled in the art also appreciates that the P code is afunction of or is encrypted by the Y code. The Y code is used to encryptthe P code. One skilled in the art appreciates that the L1 signal,containing both I & Q components, and the L2 signal can be represented,for a given satellite, i, asS _(L1i)(t)=A _(P) p _(i)(t)d _(i)(t)cos(ω₁ t)+A _(C) c _(i)(t)d_(i)(t)sin(ω₁ t), andS _(L2i)(t)=B _(P) p _(i)(t)d _(i)(t)cos(ω₂ t)

where

A_(P) and A_(C) are the amplitudes of the P and CA codes, typicallyA_(P)=2A_(C);

B_(p) is the amplitude of the L2 signal;

ω₁ and ω₂ are the L1 and L2 carrier frequencies;

p_(i)(t) represents the P(Y) ranging code and is a pseudo-randomsequence with a chip rate of 10.23 Mcbps. The P code has a period ofexactly 1 week, taking values of +1 and −1;

c_(i)(t) represents the CA ranging code and is a 1023 chip Gold code,taking values of +1 and −1; and

d_(i)(t) represents the data message, taking values of +1 and −1.

In the near future, it is expected that a third military signal,designated M-code, will be transmitted in the L1 band by GPS satellites.

A satellite constellation typically comprises 24 or more satellitesoften in similar or similarly shaped orbits but in a number of orbitalplanes. The transmissions from each satellite are on the same nominalcarrier frequency in the case of code division access satellites (suchas GPS) or on nearby related frequencies such as GLONASS. The satellitestransmit different signals to enable each one to be separately selectedeven though several satellites are simultaneously visible.

The signals from each satellite, in a CDMA system like GPS, aredistinguished from one another by means of the different spreading codesand/or differences in the spreading code rates, that is, the p_(i)(t)and c_(i)(t) sequences. Nevertheless, there remains significant scopefor interference between the signals transmitted by the satellites.Typically, the power spectrum for the CA code has maximum power at thecarrier frequency L1 and zeros at multiples of the fundamentalfrequency, 1.023 MHz, of the CA code. Therefore, it will be appreciatedthat zeros occur either side of the carrier frequency at ±1.023 MHz,±2.046 MHz etc. Similarly, the power spectrum for a the P(Y) code has amaximum amplitude centred on the L1 and L2 frequencies, with zerosoccurring at multiples of ±10.23 MHz as is expected with a sinc functionwaveform.

It is known to further modulate the ranging codes using a sub-carrier,that is, a further signal is convolved with signals similar to the Pcodes and/or CA codes, to create Binary Offset Carrier (BOC) modulationas can be appreciated from, for example, J. W. Betz, “Binary OffsetCarrier Modulation for Radionavigation”, Navigation, Vol. 48, pp227-246, Winter 2001-2002, International patent applicationPCT/GB2004/003745 and “Performance of GPS Galileo Receivers Using m-PSKBOC Signals”, Proceedings of Institute of Navigation Conference, 2003.9-12 Sep. 2003, Portland, Oreg., USA, Pratt, A. R., Owen J. I. R. all ofwhich are incorporated herein by reference. Standard BOC modulation iswell-known. The combination of a portion of a binary spreading code witha binary subcarrier signal produces the BOC signal used to modulate acarrier such as, for example, L1. The BOC signal is formed by theproduct of a binary sub-carrier (known as the spreading symbolmodulation), which is rectangular square wave, and the spreading symbols(the sequence of spreading code elements). The BOC spreading symbolmodulation can be represented as, for example,c_(i)(t)*sign(sin(2πf_(s)t)), where f_(s) is the frequency of thesubcarrier. One skilled in the art understands that BOC(f_(s),f_(c))denotes Binary Offset Carrier modulation with a subcarrier frequency off_(s) and a code rate (or chipping rate) of f_(c). Using binary offsetcarriers results in the following exemplary signal descriptions of thesignals emitted from the satellite:S _(L1i)(t)=A_(m)sc_(im)(t)m_(i)(t)d _(i)(t)cos(ω₁ t)+A _(g) sc_(ig)(t)g _(i)(t)d _(i)(t)sin(ω₁ t)=I _(SL1i)(t)+Q _(SL1i)(t), andS _(L2i)(t)=B _(m) sc _(im)(t)m _(i)(t)d_(i)(t)cos(ω₂ t)

where

A_(m), A_(g) and B_(m) are amplitudes;

m_(i)(t) is the spreading code for the in-phase (cosine) component ofthe signal;

g_(i)(t) is the spreading code for the quadrature (sine) component ofthe signal;

sc_(im)(t) represents the sub-carrier signal for m_(i)(t);

sc_(ig)(t) represents a subcarrier signal for g_(i)(t);

ω₁ and ω_(t) are designated as L1 and L2 carrier frequencies.

It will be appreciated that the embodiment expressed above uses a singlecomponent on the in-phase and a single component on the quadrature phasefor the L1 signal. Similarly, the L2 signal comprises a singlecomponent. However, one skilled in the art appreciates that the L1and/or L2 signals may use one or more components.

BOC signals are typically rectangular or square waves. However,alternatives have been proposed that involve more complex spreadingsymbol modulation utilising multiple signal levels as can be appreciatedfrom, for example, International patent application PCT/GB2004/003745,and “Performance of GPS Galileo Receivers Using m-PSK BOC Signals”,Proceedings of Institute of Navigation Conference, 2003. 9-12 Sep. 2003,Portland, Oreg., USA, Pratt, A. R., Owen J. I. R cited above. Theseprovide a means for better control of the resulting signal spectrum asthe power spectral density Φ_(n,m)(x), where x is a generalisedfrequency variable, of a BOC spreading symbol modulation is fullydefined by the equation:

${\Phi_{n,m}(x)} = {\frac{2\;\pi}{m\;\omega_{0}} \cdot \left\{ \frac{{\sin\left( \frac{\pi\; x}{2\; n} \right)} \cdot {\sin\left( \frac{\pi\; x}{m} \right)}}{\left\{ \frac{\pi\; x}{m} \right\} \cdot {\cos\left( \frac{\pi\; x}{2\; n} \right)}} \right\}^{2}}$

-   -   where x=ω/ω₀

In a subset of the multi-level digital waveforms used as spreadingsymbol modulation waveforms, a specific category has been recognisedthat has attracted the name Composite BOC (CBOC) as can be appreciatedfrom, for example, Avila-Rodriguez, J. A. et al, “Revised CombinedGalileo/GPS Frequency and Signal Performance Analysis”, Proceedings ofInstitute of Navigation Conference, 2005, 13-16 Sep. 2005, Long Beach,Calif., USA, which is incorporated herein by reference for all purposes,in which several Binary Offset Carrier signals are additively combinedto form the spreading symbol modulation waveform.

A further option for spectrum control has also arisen that usestime-multiplexed techniques in which several BOC spreading symbolmodulation waveforms are combined in a defined time sequence as can beappreciated from the above PCT application and Pratt, A. R., Owen, J. I.R., “Signal Multiplex Techniques in Satellite Channel Availability,Possible Applications to Galileo”, GNSS 2005, Institute of NavigationConference Record, pp 2448-2460, Sep. 13-16, 2005, Long Beach and Pratt,A. R. Owen, J. I. R., “Galileo Signal Optimisation in L1”, ConferenceRecord, National Technical Meeting, Institute of Navigation, pp 332-345,Jan. 24-26, 2005, San Diego. This technique assigns a specific spreadingsymbol modulation, drawn from a defined alphabet of such modulationwaveforms, one to every spreading code element (or time slot—quantisedby code element). Through the process of selecting which BOC modulationis used in which time slot, the relative proportions of each spreadingsymbol modulation component can be controlled. Only binary versions ofthis arrangement are known although it will be clear to those skilled inthe art that multi-level equivalent arrangements are also possible thatinvolve both time multiplexed techniques to determine which spreadingsymbol modulation is used in each time slot and the use of an alphabetof spreading symbol modulations that are multi-level and may be acombination of basic BOC spreading symbol waveforms. Such combinationsmay be in exemplary realisations either additive or multiplicative orsome other means for combining the base modulation waveforms.

Multiplexed BOC

A proposal has been made for several satellite navigation systems to usea common modulation spectrum so that the signals/services maintain adegree of interoperability as can be appreciated from, for example,Hein, G. W. et al, MBOC: The New Optimized Spreading Modulation forGALILEO L1 OS and GPS L1C, Conference Record, IEEE PLANS/IoN NationalTechnical Meeting, San Diego, April 2006, Session C5 Paper 7. The commonspectrum does not require different satellite navigation systems to emitwaveforms that are identical. The disclosed common spectrum, known asmultiplex BOC or MBOC, may be attained by either a time multiplextechnique or by the superposition (addition) of the required BOCcomponents. The time multiplex technique, using binary offset carriers,has become known as TMBOC, whilst the superposition technique has becomeknown as composite BOC, or by its nitial letters, CBOC.

The time multiplex method of constructing a spreading symbol modulationwaveform using BOC modulation components is illustrated in FIG. 2, whichshows a pair of signals 200. An overall BOC signal or subcarrier 202comprises a number 204 to 208 of bursts of a first spreading symbolmodulation A, each burst of which has the duration of one chip of thespreading code. There may be several successive chips with thismodulation. The overall MBOC 202 also comprises at least one burst 210of a second, distinct, spreading symbol modulation B with similarcharacteristics but having a different carrier offset frequency. Thedepicted MBOC 202 also comprises a third spreading symbol modulationburst 212, which is identified as modulation type C with yet a furthercarrier offset frequency. In the known art, each of these modulationbursts has a BOC characteristic but with a common chip rate. Prior totransmission from a navigation satellite, the carrier signal andspreading symbol modulation are further modulated by a spreading code214. It can be appreciated that only an exemplary number of chips, chipn to chip n+4, of the complete spreading code are illustrated. For thetime multiplex technique with binary offset carrier spreading symbolmodulation components, the relative magnitude of the components isdetermined by the proportion of time (in units of code sequence elementsor chips) devoted to each. In the example of FIG. 2, the proportionallotted to the first spreading symbol modulation A is ⅗, to B is ⅕ andto C is ⅕, provided that this pattern were to continue ad infinitum. Itwill be clear to those skilled in the art that other proportions arepossible within the restriction that the relative power of eachcomponent is set in multiples of 1/N, where N is the length of therepetitive spreading sequence. This restriction can be overcome also byhaving different time multiplex assignments for each repetition of thespreading sequence.

CBOC

The alternative formulation of the MBOC spectrum is by means of anadditive method, whereby two time-continuous binary offset carrierspreading symbol modulation waveforms are additively combined. FIG. 3provides an illustration 300 of the waveform produced using this method.First 302 and second 304 BOC components or waveforms are illustrated.The relative magnitudes of the two components 302 and 304 are controlledthrough the amplitudes of each of the BOC components. The first 302 BOCis the base-line BOC waveform, which is a BOC(1,1) waveform. The secondwaveform 304 illustrated a BOC(5,1) waveform. A number of chips, chip nto chip n+4, of a spreading code 306 is illustrated. The CBOC waveform308 resulting from the additive combination of the first and secondwaveforms 302 and 304 is shown. It can be appreciated that CBOC waveform308 comprises first and second components reflecting, respectively,their relationship to the first 302 and second 304 BOCs. The secondcomponent 310 is reduced in magnitude compared with the first component.For the 2 component CBOC waveform 308 shown, the resulting signalwaveform has 4 levels. In general, a CBOC waveform has 2^(n) levels whenderived from n BOC waveforms. Depending upon the relative amplitudes, itis possible that some of these levels may coincide.

Binary Offset Carrier Spreading Symbol Modulation

The conventional means of identifying the characteristics of binaryoffset carrier modulation is through 2 parameters n and m. Themodulation is denoted BOC(n,m), in which n applies to the frequency ofthe offset carrier and m refers to the chipping rate. The parameters mand n are usually associated with a GPS-like signal in which the mastersatellite clock oscillates at 10.23 MHz or some multiple or fractionthereof. The parameters may then take on the meanings expressed by:Offset carrier frequency=n×1.023 MHzChipping rate=m×1.023 M chips per second.

In the known implementation of a time multiplexed spectrum containingthe two BOC modulation components, it is known that the phase of thespreading symbol modulation is identical at the transition to each codeelement (chip). For example, if the BOC spreading symbol modulation hasa positive transition at the beginning of a specific code element,having the value +1, and a negative transition at the beginning of aspecific code element, having the value −1, then these phase assignmentsmay be applied to each spreading symbol in the complete sequence.

MBOC

One common power spectral density (PSD) that might be used by bothGalileo and GPS navigation constellations is:

$\begin{matrix}{{\Phi_{MBOC}(\omega)} = {{\frac{10}{11} \cdot {\Phi_{({1,1})}(\omega)}} + {\frac{1}{11} \cdot {\Phi_{({6,1})}(\omega)}}}} & (1)\end{matrix}$

In many satellite navigation systems, it is normal to transmit both adata-bearing signal and a ‘so-called’ pilot signal, which does not carrya data message. The data message is transmitted at a lower rate than thespreading code. For GPS CA code, the spreading code rate is 1.023 MHzwhilst the data message is transmitted at 50 bits per second. Inmodernised GPS, both the pilot and data signals are transmitted althoughnot necessarily at the same power levels. In the time multiplexed methodof generating the MBOC spectrum, there are a wide range of options forchoosing assignments for the division of power between the pilot anddata channels. This permits the option of transmitting differentrelative proportions of power for each of the BOC spreading symbolcomponents on the pilot and data-bearing signals. For example, if thetwo spreading symbol modulation components are BOC(1,1) and BOC(6,1),then the data-bearing signal, carrying a proportion γ of the totalpower, uses the BOC(1,1) spreading symbol modulation only whilst thepilot signal, carrying a proportion (1−γ) of the total power, would usea time multiplexed version having the power spectral density:

$\begin{matrix}{{{\Phi_{Pilot}(\omega)} = {{\left( {\frac{10}{11} - \gamma} \right) \cdot \left( \frac{1}{1 - \gamma} \right) \cdot {\Phi_{({1,1})}(\omega)}} + {\frac{1}{11}{\left( \frac{1}{1 - \gamma} \right) \cdot {\Phi_{({6,1})}(\omega)}}}}}\mspace{20mu}{{\Phi_{Data}(\omega)} = {\Phi_{({1,1})}(\omega)}}} & (2)\end{matrix}$

This arrangement allows considerable freedom in selecting theproportions of power allocated to the data-bearing and pilot signals andin determining how the two BOC(n,m) components are distributed betweenthese two signals. Equation (2) maintains the combined PSD for bothpilot and data-bearing signals in accordance with the required MBOC PSD.

CBOC

For the Composite BOC method, the selection of parameters to provide forpower division is more complex.

The equations that follow show the complexity associated with thecontrol of the CBOC power spectral density. It is assumed that there areat least two components in the composite BOC spectrum. For illustrativepurposes, the equations below are constructed for 2 components. However,those skilled in the art will recognise that more than 2 components maybe used.

The spectrum of a binary offset carrier, BOC(n,m), with a sine phasedspreading symbol modulation, is given in equation (3). Equation (3)shows the complex spectrum, H_(n,m)(ω), for values of (2n/m) that areeven. This corresponds to (n/m) complete cycles of the binary offsetcarrier in each spreading code symbol. The complex spectrum is based ona calculation over the duration of a single code element, ΔT=2π/(mω₀).The waveform used for the spectrum computations extends over theinterval t∈(−ΔT/2, ΔT/2) and, for definition, has a positive transitionat t=0.

$\begin{matrix}{{H_{n,m}^{\sin}(\omega)} = {\frac{2\;{\pi \cdot \left( {- 1} \right)^{({\frac{n}{m} + 1})}}}{j\; m\;\omega_{0}} \cdot \frac{{\sin\left( \frac{\pi\; x}{2\; n} \right)} \cdot {\sin\left( \frac{\pi\; x}{m} \right)}}{\left( \frac{\pi\; x}{m} \right) \cdot {\cos\left( \frac{\pi\; x}{2\; n} \right)}}}} & (3)\end{matrix}$

-   -   where x=ω/ω₀    -   and ω₀=2π·1.023·10⁶

Note that the spectrum of the sine phase BOC(n,m) waveform, H^(sin)_(n,m)(ω), consists entirely of imaginary components due to the presenceof the j (=√−1) term in the denominator.

Similarly, the spectrum of a binary offset carrier, BOC(n,m), with acosine phased spreading symbol modulation, is given in equation (3-1).Equation (3-1) shows the complex spectrum, H^(cos) _(n,m)(ω), for valuesof (2n/m) that are even. This corresponds to (n/m) complete cycles ofthe binary offset carrier in each spreading code symbol. The complexspectrum is based on a calculation over the duration of a single codeelement, ΔT=2π/(mω₀). The waveform used for the spectrum computationsextends over the interval t∈(−ΔT/2, ΔT/2) and, for definition, has apositive dwell at t=0.

$\begin{matrix}{{H_{n,m}^{\cos}(\omega)} = {\frac{2\;{\pi \cdot \left( {- 1} \right)^{({\frac{n}{m} + 1})}}}{m\;\omega_{0}} \cdot \frac{\left( {1 - {\cos\left( \frac{\pi\; x}{2\; n} \right)}} \right) \cdot {\sin\left( \frac{\pi\; x}{m} \right)}}{\left( \frac{\pi\; x}{m} \right) \cdot {\cos\left( \frac{\pi\; x}{2\; n} \right)}}}} & \left( {3\text{-}1} \right)\end{matrix}$

-   -   where x=ω/ω₀    -   and ω₀=2π·1.023·10⁶

Note that the spectrum of the cosine phased BOC(n,m) waveform, H^(cos)_(n,m)(ω), consists entirely of real components.

The corresponding power spectral density (PSD) is given in equation (4)below and is averaged over 1 second assuming that each spreading codesymbol takes a (binary) state selected randomly from the elements{+1,−1}. The PSD is:

$\begin{matrix}{{\Phi_{n,m}(x)} = {\frac{2\;\pi}{m\;\omega_{0}} \cdot \left\{ \frac{{\sin\left( \frac{\pi\; x}{2\; n} \right)} \cdot {\sin\left( \frac{\pi\; x}{m} \right)}}{\left\{ \frac{\pi\; x}{m} \right\} \cdot {\cos\left( \frac{\pi\; x}{2\; n} \right)}} \right\}^{2}}} & (4)\end{matrix}$

As discussed above, in a composite binary offset carrier (BOC) signal,as an alternative to time multiplexing, the signal is formed through theadditive combining of two or more BOC components for each spreadingsymbol. Thus, each spreading symbol has a spectrum containing, for a 2component case, a portion a of a BOC(n,m) component and a portion β of aBOC(k,m) component. Notice that both components have the same spreadingcode (chip) frequency (same duration of spreading code element). Thecomposite complex spectrum, S_(C)(ω), is then:S _(C)(ω)=H _(n,m)(ω)+β·H _(k,m)(ω)   (5)

The corresponding power spectral density is formed from the product ofS_(C)(ω) with its complex conjugate, and for real α,β:

$\begin{matrix}\begin{matrix}{{\Phi_{c}(\omega)} = {{S_{C}^{*}(\omega)} \cdot {S_{C}(\omega)}}} \\{= {{S_{C}(\omega)}}^{2}} \\{= {\left( {{\alpha \cdot {H_{n,m}^{*}(\omega)}} + {\beta \cdot {H_{k,m}^{*}(\omega)}}} \right) \cdot \left( {{\alpha \cdot {H_{n,m}(\omega)}} + {\beta \cdot {H_{k,m}(\omega)}}} \right)}} \\{= {{\alpha^{2}{\Phi_{n,m}(\omega)}} + {\beta^{2}{\Phi_{k,m}(\omega)}} + {\alpha\;{\beta\left( {{H_{n,m}^{*} \cdot H_{k,m}} + {H_{n,m} \cdot H_{k,m}^{*}}} \right)}}}}\end{matrix} & (6) \\{{where}{{\Phi_{n,m}(\omega)} = {{H_{n,m}^{*}(\omega)} \cdot {H_{n,m}(\omega)}}}{and}{{\Phi_{k,m}(\omega)} = {{H_{k,m}^{*}(\omega)} \cdot {H_{k,m}(\omega)}}}} & \;\end{matrix}$

Equation (6) clearly shows the differences in PSDs of the composite BOC(additive waveforms) and time multiplex approaches. The power spectraldensity, Φ_(TM)(ω), for the time multiplex of BOC(n,m) and BOC(k,m)spreading symbol components, if the proportions are α² and β², is:Φ_(TM)(ω)=α²·Φ_(n,m)(ω)+β² Φ_(k,m)(ω)   (7)

Therefore, the time multiplex sequence comprises α²/(α²+β²) chips with apower spectral density of Φ_(n,m)(ω) and β²/(α²+β²) chips with a powerspectral density of Φ_(k,m)(ω). The difference between the PSDs for CBOCand TMBOC techniques reside in the presence of the cross spectral termsin the CBOC PSD, Φ_(cross)(ω):Φ_(cross)(ω)=αβ(H _(n,m) *·H _(k,m) +H _(n,m) ·H _(k,m)*)   (8)

The situation is exacerbated when, for example, there are 3 componentsforming the composite signal. In the time multiplex realisation, thecomponents are interspersed amongst the code elements in suitablenumbers to establish the contributory proportions required from each inthe power spectral density to be transmitted (more correctly at the timeof signal generation as there are transmission filters in the satellitesthat control out of band emissions). A typical example has theproportions α²,β²,δ² for signals with each of three PSD's as equation(9) below illustrates.Φ_(TM)(ω)=α²·Φ_(n,m)(ω)+β²·Φ_(k,m)(ω)+δ²·Φ_(l,m)(ω)   (9)

The corresponding spectrum for the additive method of producing a 3component composite BOC signal has three cross spectral terms of theform of equation (9).

$\begin{matrix}\begin{matrix}{{\Phi_{C}(\omega)} = {{S_{C}^{*}(\omega)} \cdot {S_{C}(\omega)}}} \\{= {\left( {{\alpha \cdot {H_{n,m}^{*}(\omega)}} + {\beta \cdot {H_{k,m}^{*}(\omega)}} + {\delta \cdot {H_{l,m}^{*}(\omega)}}} \right) \cdot}} \\{\left( {{\alpha \cdot {H_{n,m}(\omega)}} + {\beta \cdot {H_{k,m}(\omega)}} + {\delta \cdot {H_{l,m}(\omega)}}} \right)} \\{= {{\alpha^{2}{\Phi_{n,m}(\omega)}} + {\beta^{2}{\Phi_{k,m}(\omega)}} + {\delta^{2}{\Phi_{l,m}(\omega)}} +}} \\{{\alpha\;{\beta\left( {{H_{n,m}^{*} \cdot H_{k,m}} + {H_{n,m} \cdot H_{k,m}^{*}}} \right)}} +} \\{{\alpha\;{\delta\left( {{H_{n,m}^{*} \cdot H_{l,m}} + {H_{n,m} \cdot H_{l,m}^{*}}} \right)}} +} \\{{\beta\;{\delta\left( {{H_{k,m}^{*} \cdot H_{l,m}} + {H_{k,m} \cdot H_{l,m}^{*}}} \right)}}\;}\end{matrix} & (10) \\{{where}{{\Phi_{n,m}(\omega)} = {{H_{n,m}^{*}(\omega)} \cdot {H_{n,m}(\omega)}}}{{\Phi_{k,m}(\omega)} = {{H_{k,m}^{*}(\omega)} \cdot {H_{k,m}(\omega)}}}{{\Phi_{l,m}(\omega)} = {{H_{l,m}^{*}(\omega)} \cdot {H_{l,m}(\omega)}}}} & \;\end{matrix}$

The cross-spectral terms in equation (10) have a significant influenceon the transmitted PSD. Clearly, the presence of the cross spectralterms hinders the realisation of a common PSD for CBOC and MBOC.

It is an object of embodiments of the present invention to at leastmitigate one or more problems of the prior art.

SUMMARY OF THE INVENTION

Accordingly, embodiments of the present invention provide a method ofgenerating a signal comprising the steps of generating at least firstand second portions of the signal; the first portion being derived from,or at least having characteristics of, at least first respectiveportions of at least first and second signals having a first phase stateand the second portion being derived from, or having characteristics of,at least second respective portions of said at least first and secondsignals having a second phase state that is complementary to the firstphase state.

Advantageously, when averaged over, for example, two chips or some othertime period or interval, the composite complex spectrum for thecombination of the two modulating subcarriers comprises at leastsubstantially reduced, and preferably substantially eliminated, crossspectral terms. This allows, for example, the spectrum of a modulatingsubcarrier such as, for example, a composite BOC signal, to havesubstantially the same power spectral density (PSD) as a differentmodulating subcarrier such as, for example, a time division multiplexBOC when considered in terms of whether or not the power spectra of bothcomprise cross spectral terms.

A further embodiment provides a method of generating a CBOC waveform orspreading modulation waveform from first and second BOC waveforms, theCBOC waveform having a predetermined power spectral density comprisingat least reduced cross spectral terms of the power spectral densities ofthe first and second BOC waveforms averaged over at least twopredetermined time intervals such as, for example, at least two chips;the method comprising the steps of arranging for the states of the firstand second BOC signals over a subsequent predetermined time interval ofthe at least two predetermined time intervals to be complementary to thestates of the first and second BOC signals over a current predeterminedtime interval of the at least two predetermined time intervals.

Another embodiment provides a signal generator comprising means togenerate at least a subsequent portion of a signal relative to at leasta current portion of a signal; the current portion being derived from,or at least having characteristics of or associated with, at leastcurrent respective portions of at least first and second signals havinga first phase state, the means to generate comprising means to combineat least subsequent portions of the at least first and second signalshaving a phase state that is complementary to the first phase state.

An embodiment provides a signal generator for generating a CBOC waveformfrom first and second BOC waveforms, the CBOC waveform having apredetermined power spectral density comprising at least reduced crossspectral terms of the power spectral densities of the first and secondBOC waveforms averaged over at least two predetermined time intervals;the generator comprising means to arrange for the states of the firstand second BOC signals over a subsequent predetermined time interval ofthe at least two predetermined time intervals to be complementary to thestates of the first and second BOC signals over a current predeterminedtime interval of the at least two predetermined time intervals.

Embodiments provide a signal comprising at least a subsequent portion ofthe signal relative to at least a current portion of the signal; thecurrent portion being derived from, or having characteristics of orassociated with, at least current respective portions of at least firstand second signals having a first phase state such that the phase stateof at least subsequent portions of the at least first and second signalsassociated with said at least a subsequent portion is complementary tothe first phase state.

Embodiments of the present invention can be realised in the form ofhardware, software or a combination thereof. Suitably, an aspect ofembodiments of the present invention provides a computer programcomprising executable instructions for implementing a method, system,apparatus, generator or generating a signal according to embodiments ofthe invention. Furthermore, such a computer program can be stored usingany form of storage such as, for example, optically or magneticallyreadable media, chips, ROMs, PROMs and other volatile or non-volatiledevices. Suitably, embodiments of the present invention providemachine-readable storage storing such a computer program.

In current proposals between several different navigation satelliteoperators (such as USA with GPS and the European Union with Galileo),there are public documents that give effect to a recommendation bymutual technical working groups to use a common PSD for each system'semissions in the L1 RNSS band. This may not require the implementationof the same time waveform. Embodiments of the present invention allowthe above common PSD for each system's emissions in the L1 RNSS band tobe realized.

In a further aspect of the invention, a second method is used toeliminate the cross spectral term in equation 6. This has the sameeffect as the other methods but is an alternative implementation. Thecross spectral term, Φ_(cross)(ω), can be set to zero if the followingcondition is met:(H _(n,m) *·H _(k,m) +H _(n,m)·H _(k,m)*)=0 or equivalentlyH _(n,m) *·H _(k,m) =−H _(n,m) ·H _(k,m)*

This condition can be satisfied by having the BOC(n,m) spectra made upof purely imaginary components whilst the BOC(k,m) spectra consists ofpurely real components. Therefore, under such a condition the complexconjugate of H^(sin) _(n,m), isH _(n,m) ^(sin) =−H _(n,m) ^(sin)whilst the complex conjugate of H^(cos) _(k,m) does not change sign:H _(k,m) ^(cos) *=+H _(k,m) ^(cos)

Note that the superscripts sin and cos have been added to define thephasing of the sub-carrier in the binary offset carrier spreading symbolmodulation. This arrangement satisfies the condition required toeliminate the cross spectral term. This embodiment of the inventionrequires that the two BOC components have phasing substantially inquadrature, one being of sine phasing and the other component being ofcosine phasing.

In a still further aspect of embodiments of the invention there areprovided receiver architectures are identified for processingtransmitted signals identified herein. Embodiments can be realised thathave a single channel to processes all signal components substantiallysimultaneously. Alternatively, or additionally, embodiments can berealised that have multiple channels so that the individual signalcomponents are processed separately by respective channels. One skilledin the art will realise that such processing may not necessarily beoptimised to provide the maximum signal to noise ratio.

BRIEF DESCRIPTION OF THE DRAWINGS

Embodiments of the present invention will now be described, by way ofexample only, with reference to the accompanying drawings.

FIG. 1 illustrates a transmitter or signal generator;

FIG. 2 depicts a known time division multiplexed binary offset carrier(MBOC);

FIG. 3 shows a known composite binary offset carrier (CBOC);

FIG. 4 shows a CBOC signal according to an embodiment of the presentinvention;

FIG. 5 illustrates a conventional schematic system for generating a CBOCwaveform;

FIG. 6 depicts a schematic system for generating a CBOC waveformaccording to an embodiment of the present invention;

FIG. 7 depicts a schematic system to generate a CBOC waveform accordingto embodiments of the present invention that uses the spreading codeepoch to control phase inversion;

FIG. 8 depicts a variant of the schematic system for generating a CBOCwaveform as illustrated in FIG. 7;

FIG. 9 shows a further embodiment of a schematic system for generating aspreading symbol modulation waveform according to an embodiment;

FIG. 10 illustrates a still further embodiment of a schematic system forgenerating a CBOC waveform;

FIG. 11 shows an embodiment of a receiver; and

FIG. 12 depicts an embodiment of a further CBOC signal.

DESCRIPTION OF EMBODIMENTS

Referring to FIG. 1, there is shown, schematically, a transmitter 100according to an embodiment of the present invention. The transmitter 100comprises means 102, that is, a generator, for generating or selectingranging codes for transmission. It will be appreciated by those skilledin the art that such ranging codes may be generated by, for example,shift register implementations. An alternative to generation by means ofa shift register may be through replaying the sequence of code statescomprising the code sequence from a memory device adapted tocontinuously replay such sequences. It can be appreciated that theranging code selection and/or generation means 102 is illustrated asproducing g_(i)(t) and m_(i)(t). These codes are fed to respectivemixers 104 and 106. The mixers 104 and 106 are arranged to combine theranging codes with subcarriers according to embodiments of the presentinvention. Respective subcarrier generators 108 and 110 generate thesubcarriers. Optionally, a data signal, d_(i)(t), is also preferablymixed with the ranging codes and subcarriers. The duration of one bit ofthe data signal is normally an integer multiple of the code repetitioninterval. For example, in GPS CA code, it is 20 times the 1 ms coderepetition interval, that is, the data rate is 50 bps. The mixed signals112 and 114 are fed to a further pair of mixers 116 and 118, where theyare mixed with in-phase and quadrature phase signals produced via anoscillator and phase shifter assembly 120 and 121. The further mixedsignals 122 and 124 are combined, via a combiner 126, and are output forsubsequent up conversion by an appropriate up converter 128. The outputfrom the up converter 128 is fed to a high-power amplifier 130 and thenfiltered by an appropriate filter 133 for subsequent transmission by,for example, a satellite or other device arranged to emit or transmitthe ranging codes.

In a preferred embodiment, the operation of the invention involves thesequencing of the relative phases of the binary offset carriergenerators for the additive combining method in such a way as to providea variety of different power spectral densities, one for each phaseassignment. Such an assignment is, in the first instance, valid for theduration of a single code element or chip. Over the duration of severalcode elements, or over the complete code sequence, each possible phaseassignment (and corresponding power spectrum) is generated a pre-definednumber of times. The resulting power spectral density corresponds to theaverage PSD of all those generated. Therefore, it is possible to cancelthe signals arising from the cross spectral terms in the resultingcomposite BOC spectrum. This operation can be performed with as manycomponents as required in the composite BOC spectrum. Consequently, theaverage PSD may be arranged to be identical with that of the timemultiplex arrangement of the BOC spreading symbol modulation.

For a two component composite, there are only two distinct phaseassignments for α and β as follows in table 1. The product of α and β isidentified as a ‘phase assignment operator.

TABLE 1 Phase Assignment of α and β Phase β = + β = − α = + + − α = − −+

According to this table, if half of the BOC(n,m) and BOC(k,m) aregenerated with the same phase assignment from the phase assignmentoperator (αβ=+1) and half with opposite phase from the phase assignmentoperator (αβ=−1), the average PSD is:

$\begin{matrix}\begin{matrix}{{{\Phi_{C}(\omega)}}_{ave} = {{0.5 \cdot {S_{C++}^{*}(\omega)} \cdot {S_{C++}(\omega)}} + {0.5 \cdot {S_{C + -}^{*}(\omega)} \cdot {S_{C + -}(\omega)}}}} \\{= {0.5 \cdot \left( {{{S_{C++}(\omega)}}^{2} + {{S_{C + -}(\omega)}}^{2}} \right)}} \\{= {{\alpha^{2}{\Phi_{n,m}(\omega)}} + {\beta^{2}{\Phi_{k,m}(\omega)}} +}} \\{{0.5\;\alpha\;{\beta\left( {{H_{n,m}^{*} \cdot H_{k,m}} + {H_{n,m} \cdot H_{k,m}^{*}}} \right)}} -} \\{0.5\;\alpha\;{\beta\left( {{H_{n,m}^{*} \cdot H_{k,m}} + {H_{n,m} \cdot H_{k,m}^{*}}} \right)}} \\{= {{\alpha^{2}{\Phi_{n,m}(\omega)}} + {\beta^{2}{\Phi_{k,m}(\omega)}}}}\end{matrix} & (11)\end{matrix}$

As can be observed from equation (11), the phase assignment of the BOCgenerators controls the resulting spectrum. By allocating 50% to eachphase assignment, the resulting cross spectral term is cancelled. Thebenefit of this arrangement is that the PSD of the composite BOC(additive combination) is composed just of the PSD's of each of theconstituents only, and in whatever proportions (α,β) are required. Ifrequired, a portion of the cross power spectral term could be retainedthrough changing the proportions of the positive and negative phaseassignment operator.

The definition of the phase of the BOC generators is made at the instantcorresponding to the centre of the spreading code symbol modulation. Thephase assignment is common to the complete spreading symbol. Itcorresponds to a common direction of the signal transition at thecentral instant of a spreading symbol as illustrated in FIG. 3 at 312 to320. For a first preferred embodiment using 2 BOC generators, thespectrum of the output for a combined code and data state of {+1}, phasestate of {+1}, is

$\begin{matrix}{{{H_{C}(\omega)} = {{\alpha\;\Phi_{n}{H_{n,m}(\omega)}} + {\beta\;\phi_{k}{H_{k,m}(\omega)}}}}{{H_{n,m}(\omega)} = {\frac{2\;{\pi \cdot \left( {- 1} \right)^{({\frac{n}{m} + 1})}}}{j\; m\;\omega_{0}} \cdot \frac{{\sin\left( \frac{\pi\; x}{2\; n} \right)} \cdot {\sin\left( \frac{\pi\; x}{m} \right)}}{\left( \frac{\pi\; x}{m} \right) \cdot {\cos\left( \frac{\pi\; x}{2\; n} \right)}}}}{{H_{k,m}(\omega)} = {\frac{2\;{\pi \cdot \left( {- 1} \right)^{({\frac{k}{m} + 1})}}}{j\; m\;\omega_{0}} \cdot \frac{{\sin\left( \frac{\pi\; x}{2\; k} \right)} \cdot {\sin\left( \frac{\pi\; x}{m} \right)}}{\left( \frac{\pi\; x}{m} \right) \cdot {\cos\left( \frac{\pi\; x}{2\; k} \right)}}}}} & (12)\end{matrix}$

-   -   where x=ω/ω₀        φ_(n),φ_(k) ∈ {+1,−1}, and        ω₀=2π·1.023·10⁶        and the corresponding PSD is:

$\begin{matrix}\begin{matrix}{{\Phi_{C}(\omega)} = {\left( {{{\alpha \cdot \phi_{n}}{H_{n,m}^{*}(\omega)}} + {{\beta \cdot \phi_{k}}{H_{k,m}^{*}(\omega)}}} \right) \cdot}} \\{\left( {{{\alpha \cdot \phi_{n}}{H_{n,m}(\omega)}} + {{\beta \cdot \phi_{k}}{H_{k,m}(\omega)}}} \right)} \\{= {{\alpha^{2}{\Phi_{n,m}(\omega)}} + {\beta^{2}{\Phi_{k,m}(\omega)}} +}} \\{\alpha\;\beta\;\phi_{n}{\phi_{k}\left( {{H_{n,m}^{*} \cdot H_{k,m}} + {H_{n,m} \cdot H_{k,m}^{*}}} \right)}}\end{matrix} & (13) \\{{{{and}\mspace{14mu}{where}},{{as}\mspace{14mu}{before}},{{\Phi_{n,m}(\omega)} = {{H_{n,m}^{*}(\omega)} \cdot {H_{n,m}(\omega)}}}}{{\Phi_{k,m}(\omega)} = {{H_{k,m}^{*}(\omega)} \cdot {H_{k,m}(\omega)}}}} & \;\end{matrix}$

It can be observed from equation 11 that the presence of the phaseassignment switches does not affect the presence, or signs, of the powerspectral densities for the BOC(n,m) or BOC(k,m) components, Φ_(n,m)(ω),Φ_(k,m)(ω). However, the product of the phase assignments, φ_(n)φ_(k),which can take the values of +1 or −1, controls the sign of the crossspectral term. Consequently, by selecting phase assignment settings thatcause the phase term to be positive or negative, power spectraldensities as in equation 12 may be formed as follows.

$\begin{matrix}{{{{for}\mspace{14mu}\phi_{n}},{\phi_{k} = {+ 1}},{{+ 1}\mspace{14mu}{or}\mspace{14mu}\phi_{n}},{\phi_{k} = {- 1}},{- 1}}\begin{matrix}{{\Phi_{C}^{++}(\omega)} = {\Phi_{C}^{--}(\omega)}} \\{= {\left( {{{\alpha \cdot \phi_{n}}{H_{n,m}^{*}(\omega)}} + {{\beta \cdot \phi_{k}}{H_{k,m}^{*}(\omega)}}} \right) \cdot}} \\{\left( {{{\alpha \cdot \phi_{n}}{H_{n,m}(\omega)}} + {{\beta \cdot \phi_{k}}{H_{k,m}(\omega)}}} \right)} \\{= {{\alpha^{2}{\Phi_{n,m}(\omega)}} + {\beta^{2}{\Phi_{k,m}(\omega)}} +}} \\{\alpha\;{\beta\left( {{H_{n,m}^{*} \cdot H_{k,m}} + {H_{n,m} \cdot H_{k,m}^{*}}} \right)}}\end{matrix}} & (14) \\{{{{for}\mspace{14mu}\phi_{n}},{\phi_{k} = {+ 1}},{{- 1}\mspace{14mu}{or}\mspace{14mu}\phi_{n}},{\phi_{k} = {- 1}},{+ 1}}\begin{matrix}{{\Phi_{C}^{+ -}(\omega)} = {\Phi_{C}^{+ -}(\omega)}} \\{= {{\alpha^{2}{\Phi_{n,m}(\omega)}} + {\beta^{2}{\Phi_{k,m}(\omega)}} -}} \\{\alpha\;{\beta\left( {{H_{n,m}^{*} \cdot H_{k,m}} + {H_{n,m} \cdot H_{k,m}^{*}}} \right)}}\end{matrix}} & \;\end{matrix}$

Thus, by combining an equal number of signals with each of the PDS's inequation 12 and having substantially complementary phase assignments, itcan be arranged that the PSD of the combined signal, after averagingover an interval, exhibits no cross spectral terms. Alternatively, bysimilar combining with an unequal number of terms, a required percentageof the cross spectral term can be retained.

There are a number of ways in the BOC signals can be processed to haveequal (or if required, unequal) numbers of complementary phaseassignments.

A first embodiment uses a phase alternation approach whereby the initialphase of one of the BOC(n,m) and BOC(k,m) signals is alternated for eachchip of the spreading code signal. In this case, the averaging intervalis just 2 code chips as there will have been one chip where the spectrumhas the characteristic of Φ⁺⁺c(ω) or Φ⁻⁻ _(C)(ω) and one chip with thespectrum of Φ⁺⁻(ω) or Φ⁺⁻ _(C)(ω).

Referring to FIG. 4, there is shown a number of waveforms 400 forgenerating a CBOC waveform 402 having a power spectral density withsubstantially zero cross spectral terms that usually arise whencombining a first BOC(n,m) waveform 404 and a second BOC(k,m) waveform406. In the illustrated embodiment, the first BOC of waveform 404 is aBOC (1, 1). However, it can be appreciated that other BOC waveforms canequally well be used. The second BOC waveform 406 is a BOC (5, 1).However, again, it will be appreciated that other BOC waveforms can beused to realise embodiments of the present invention such as, forexample, those described in the above referenced technical papers andinternational patent application. Embodiments of the invention are notlimited to either BOC(1,1) or BOC(5,1). In the following examples,BOC(6,1) will be used instead of BOC(5,1).

FIG. 4 comprises a number of the dotted lines 408 to 416 that representpre-determinable points of the waveforms 404 and 406. It can beappreciated that, for the purposes of illustration only, the dottedlines 408 to 416 are shown as being at the midpoint of the BOC chips. Itcan be appreciated that the negative going transition within the firstchip, chip n, is coincidental with a negative going transition withinthe first chip period of the second BOC waveform 406. For the purposesof the present application, such an alignment and agreement oftransitions of the BOC waveforms 404 and 406 at the pre-determinablepoints, that is, the midpoints in the present embodiment, is such thatthe waveforms are said to be in phase or to have the same phase state orcondition. Therefore, a negative going transition of the first BOCwaveform 404 coinciding with a negative going transition of the secondBOC waveform406 are said to be in phase or to have a (−, −) phase stateor condition. The converse is also true, that is, coincident positivegoing transitions are also said to be in phase or to have a (+, +) phasestate or condition. It should be noted for the purposes of the presentapplication that the phase states (+, +) and (−, −) are substantiallyidentical. Coincidence between a positive going transition of the firstBOC waveform 404 and a negative going transition of the second BOCwaveform 406 are such that the first and second BOC waveforms 404 and406 are said to be out of phase or in anti-phase. The correspondingphase state or condition is (+, −). The converse is also true, that is,a negative going transition of the first BOC waveform 404 and a positivegoing transition of the second BOC waveform 406 are said to have a phasestate or condition (−, +) and the first and second BOC waveforms 404 and406 are said to be out of phase or in anti-phase. It can be appreciatedfrom the illustrated embodiment that none of the BOC waveforms for theillustrated chip periods are out of phase. All have a (+,+) phase state.Those skilled in the art will recognise that the equivalent of suchphase changes from (+,+) to (−,−) and from (+,−) to (−,+) can also occuras a result of changes in the spreading code state 420 or data symbolstate 422.

Additively combining the first and second BOC waveforms 404 and 406would, but for the present invention clearly result in the waveform 308shown in FIG. 3. However, signals according to a first embodiment of thepresent invention are arranged such that the cross spectral terms of thepower spectrum of the summation of the first 404 and second 406 BOCwaveforms for a number of given chips period are cancelled or averagedout by ensuring that the cross spectral terms of the power spectrum ofthe summation of the first 404 and second BOG waveforms of a subsequentchip period are complementary, that is, have phases arranged to at leastreduce the effects of, and, preferably, to cancel substantiallyentirely, the former cross spectral terms. This is achieved by ensuringthat the first 404 and second 406 BOG waveforms of the subsequent chipperiod have the opposite phase state or condition to the phase state orcondition of the BOC waveforms 404 and 406 of an earlier chip period.

This is achieved in the illustrated embodiment by the second BOCwaveform 406 such that the waveform shown in 418 results. Referring tothe modified BOC waveform 418 and the first BOC waveform 404, it can beappreciated that the phase states or conditions alternate between inphase, that is, (+, +), and out of phase or anti-phase, that is, (+, −).Therefore, combining the first of BOC waveform 404 and the modifiedsecond BOC waveform 418 produces the composite BOC waveform 402 with adesirable power spectral density. The power spectral density of the CBOCdoes not contain cross spectral terms relating to the first BOC waveform404 and the second BOC waveform 406. Therefore, it can be appreciatedthat the power spectral density of the CBOC waveform 402 substantiallycorresponds to that of an MBOC signal.

In general, providing that, on average, the in phase portions of thefirst 404 and second 406 BOC waveforms are balanced by an equal orcorresponding number of out of phase portions of the first 404 and thesecond 406 BOC waveforms, there should be a zero net cross productcontribution to the power spectral density.

FIG. 5 shows a schematic system 500 for producing a composite BOC signal502 according to the prior art. A pair of BOC waveforms 504 and 506, BOC(n,m) and BOC (k,m), optionally scaled, via scalers 508 and 510, priorto combining, are combined using an adder 512. A multiplier 514 is usedto combine the BOC subcarrier 502 (CBOC) with a spreading code 516. Thepower contributions of the pair of BOC waveforms are controlled by thescalers 508 and 510 using coefficients γ and (1−γ).

Referring to FIG. 6, there is shown a schematic system 600 for producinga CBOC waveform or spreading symbol modulation waveform according to anembodiment of the present invention. The system 600 comprises a pair ofBOC waveform generators 602 and 604 for producing respective BOCwaveforms, BOC(n,m) 606 and BOC(k,m) 608. Optionally, the waveforms 606and 608 are scaled, via scalers 610 and 612 or some appropriate means,according to desired power contributions of the BOC waveforms 606 and608 to the composite waveform 614, that is, to the CBOC waveform 614.

The inversion or change of phase state or condition of the BOC waveforms606 and 608 is controlled by appropriate selection of the coefficients αand β together with respective multipliers 616 and 618 and generators620 and 622. It will be appreciated that the system 600 illustratedrepresents the general case. In practice, only one of the BOC waveformswill be inverted at any one time and, accordingly, the firstcoefficient, a, for example, can generally be fixed or set to +1. TheBOC waveforms 624 and 626 having selected phases are combined via anadder 628 to produce the CBOC waveform 614.

Typically, the CBOC waveform 614 is multiplied, via a multiplier 630,with a spreading waveform 632 produced via a spreading waveformgenerator 634. The spreading code generator 634 is driven by anoscillator or code chipping rate generator 636. Embodiments of thepresent invention can be realised in which at least one of the α and βgenerators are responsive to the code generator clock chipping rate 638or multiples thereof.

Referring to FIG. 7, there is shown a schematic system 700 for producinga CBOC waveform or spreading symbol modulation waveform according to anembodiment of the present invention. The system is substantially similarto that described with reference to FIG. 6, but for the phase inversionor phase state/condition being controlled by or being responsive to thespreading waveform/code epochs. The system 700 comprises a pair of BOCwaveform generators 702 and 704 for producing respective BOC waveforms,BOC(n,m) 706 and BOC(k,m) 708. Optionally, the waveforms 706 and 708 arescaled, via scalers 710 and 712 or some appropriate means, according todesired power contributions of the BOC waveforms 706 and 708 to thecomposite waveform 714, that is, to the CBOC waveform 714.

The inversion or change of phase state or condition of the BOC waveforms706 and 708 is controlled by appropriate selection of the coefficients αand β together with respective multipliers 716 and 718 and generators720 and 722. It will be appreciated that the system 700 illustratedrepresents the general case. In practice, only one of the BOC waveformswill be inverted at any one time and, accordingly, for example, thefirst coefficient, a, can generally be fixed or set to +1. The BOCwaveforms 724 and 726 having selected phases are combined via an adder728 to produce the CBOC waveform 714. Typically, the CBOC waveform 714is multiplied, via a multiplier 730, with a spreading code 732 producedvia a spreading code generator 734. The spreading code generator 734 isdriven by an oscillator 736. The spreading code has an associatedplurality of regularly spaced epochs 738. The sign, that is, {+1,−1}, ofβ is changed at the start of every code period, that is, every epoch, orcode chip period. The duration of the states of β correspond to theduration of a code element or chip. However, embodiments can be realisedin which the phase of the sign alternation can be set to occur otherthan at the start of every code period. Still further, embodiments canbe realised in which the state of β changes at multiples or fractions ofthe code period.

Referring to FIG. 8 there is depicted a schematic system 800 forgenerating a CBOC waveform according to an embodiment of the presentinvention. The system 800 is the linear system equivalent to thatdepicted in, and described with reference to, FIG. 7. Two BOC waveforms802 and 804 are generated via respective BOC waveform generators 806 and808. The waveforms 802 and 804 are optionally scaled, via scalers 810and 812, according to desired respective power contributions to the CBOCwaveform 814. The scaled BOC waveforms 816 and 818 are multiplied, viarespective multipliers 820 and 822, by the α and β coefficientsaccording to desired relative phases or phase states over at least acurrent chip, or other interval, as compared a phase state or conditionof the BOC waveforms of over a previous chip or other interval. Theresulting waveforms 824 and 826 are multiplied, via respectivemultipliers 828 and 830, by spreading waveforms 832 and 834 generated byrespective spreading waveform generators 836 and 838. The CBOC waveform814 is produced by summing the waveforms 840 and 842 using a combiner844.

It should be noted that a second preferred embodiment may be realised byunderstanding that the combination of the spreading code generator 838and the β generator can be replaced by a new spreading code generatorproducing sequence B, as opposed to sequence A. Accordingly, thecombination of the β coefficient, multiplier 822, spreading waveformgenerator 838 and multiplier 830 can be replaced by a correspondingspreading code generator 846 as is shown in FIG. 8. This requires thespreading waveforms produced by the first and second spreading codegenerators 836 and 846 to be substantially statistically independentrandom waveforms such that, on average, the number of (+,+) and (−,−)phase states are balanced by the number of (+.−) and (−,+) phase states.If some proportion of the cross spectral terms are required, then the(+,+) and (−,−) phase states do not need to balance the number of (+,−)and (−,+) phase states. The desired proportion of the cross spectralterms is influenced by the level of imbalance.

Referring to FIG. 9, there is shown a schematic system 900 for producinga spreading symbol modulation waveform according to an embodiment of thepresent invention. The system is substantially similar to that describedwith reference to FIG. 6, but for the phase inversion or phasestate/condition being controlled by or being responsive to the datasymbol period or multiples or fractions thereof. The system 900comprises a pair of BOC waveform generators 902 and 904 for producingrespective BOC waveforms, BOC(n,m) 906 and BOC(k,m) 908.

Optionally, the waveforms 906 and 908 are scaled, via scalers 910 and912 or some appropriate means, according to desired power contributionsof the BOC waveforms 906 and 908 to the composite waveform 914, that is,to the spreading symbol modulation waveform 914.

The inversion or change of phase state or condition of the BOC waveforms906 and 908 is controlled by appropriate selection of the coefficients αand β together with respective multipliers 916 and 918 and generators920 and 922. It will be appreciated that the system 900 illustratedrepresents the general case. In practice, only one of the BOC waveformswill be inverted at any one time and, accordingly, for example, thefirst coefficient, a, can generally be fixed or set to +1. The BOCwaveforms, having selected or determined phases, 924 and 926 arecombined via an adder 928 to produce the CBOC waveform 914. Typically,the CBOC waveform 914 is multiplied, via a multiplier 930, with aspreading code 932 produced via a spreading code generator 934. Thespreading code generator 934 is driven by an oscillator 936. The sign,that is, {+1,−1}, of β is changed every data symbol period or multiplesor fractions thereof.

The waveform resulting combination of the CBOC waveform 914 and thespreading waveform 932 is multiplied by a data signal 940 using amultiplier 942 to produce a combination of the CBOC waveform, thespreading code signal and the data signal.

It can be appreciated that embodiments can be realised that employ aseparate code sequence for the BOC(n,m) and BOC(k,m) spreading symbolmodulation. The duration of the code sequence is identical for the twospreading symbol modulations in this example but this is not necessary.For example, embodiments can be realised in which one of the spreadingcode generators has a period that is a multiple of the period of otherspreading code generator. Furthermore, embodiments can be realised inwhich the lengths of the spreading code sequences do not have a rationalnumber relationship. The spreading codes are normally selected from thesame family but this is also not a necessity. In order to cause theaverage spectrum to exhibit substantially zero cross spectral terms, thetwo codes should have characteristics of independent random sequences sothat their mutual cross correlation (at zero time offset) issubstantially zero. This is true also for embodiments described withreference to FIGS. 6 to 8. The averaging time for the spectrum for theembodiments described with reference to FIG. 9 is the duration of thecode sequence. If the two code generators have different sequencelengths, then a suitable averaging time can usually be found. In thelimit, this would be a duration such that both of the sequences hadreturned to their respective starting positions (having a sequencelength that is the lowest common multiple of the divisors of theindividual sequence lengths). However, substantially acceptable resultscan usually be obtained for shorter intervals than the longest commonmultiple of the 2 code sequences.

Further embodiments can be realised that influence the correlationbetween the BOC(n,m) and BOC(k,m) spreading symbol modulation. Thistechnique employs a (slow) binary data modulation combined, preferablymultiplicatively, onto one of the spreading modulation components. Thishas the same effect as alternating the phase assignments as in aboveembodiments but over the much longer period of many data bit durations

Such an embodiment is schematically depicted in FIG. 10. The system 1000illustrated in FIG. 10 comprises first and second BOC waveformgenerators 1002 and 1004 producing respective BOC waveforms 1006 and1008. The BOC waveforms, BOC(n,m) and BOC(k,m), are optionally scaled todetermine their respective power contributions to the CBOC waveform1010. The scaled waveforms 1012 and 1014 are combined, via respectivemultipliers 1016 and 1018, with respective spreading codes 1020 and 1022produced via respective spreading code generators 1024 and 1026. The BOCwaveforms, used as spreading symbol modulation waveforms, 1028 and 1030are combined with respective data signals 1032 and 1034 to produce theoverall combined spreading symbol, code symbol and data modulationwaveform. This used as the base-band modulation for up-conversion to thedesired carrier frequency for transmission. However, it is a conditionthat the data signals are sufficiently random to influence, andpreferably eliminate, the cross spectral terms within the combinedcomplex power spectrum.

Embodiments can be realised in which variable modulus signal andconstant signal envelopes are used. It will be appreciated that anyconstraints that are aimed at preserving unitary or constant magnitudeof (I²+Q²)^(1/2) need not necessary apply if a variable modulus signalenvelope is desired or is acceptable.

FIG. 11 shows an embodiment of a receiver 1100 adapted to process thesignals arising from the transmission of multiplexed binary offsetcarrier signals. The signals transmitted from each satellite in thevisible constellation are received at an antenna 1102, and are processedin an RF processor 1104, which amplifies, filters and frequency changesthe signals as is known in the prior art. The output 1106 of the RFprocessor is connected to a digitiser 1108 that produces digitisedreceived signal samples 1110.

The digitised received signal samples 1110 are applied in the exemplaryembodiment to a correlation processor 1112, which correlates thedigitised received signal samples 1110 with a group of replica signals1114, produced by a signal replica generator 1116, in a correlation bank1118. The specific form of the replica signals 1114 depends on the typeof signals being received and the chosen option for subsequentprocessing. For example, for the Combined Binary Offset

Carrier signal, known as CBOC, a multi-level replica signal may be usedcombining a residual carrier signal, a code signal and the binarysubcarrier modulation. The code and binary subcarrier modulation areprovided in early, prompt, very early, late and very late forms and withcarrier signal versions being in both in-phase and quadraturerelationship with a receiver carrier reference oscillator (not shown)that forms part of the signal replica generator , 1104.

Preferably, also included in the signal replica generator 1116, inaddition to the carrier replica generator, are a code replica generatorand a sub-carrier replica generator. The outputs of the individualelements of the replica generator are combined to form the saidcomposite binary offset carrier signal.

In a separate aspect of the invention, an embodiment of a compositebinary offset carrier signal can be realised as a time multiplexedsignal whereby separate parts of the modulation are transmitted in atime sequence. One realisation of such a signal has two portions of amultilevel modulation waveform transmitted in a specific time sequence.Specific embodiments of such signals are shown in FIG. 12, where eachsignal has two components of the multilevel modulation waveform. Thefirst of the replica waveforms 1202 is a tertiary spreading symbolconsisting of the levels 0, +1, 0, −1, 0 in sequence. There are 3spreading symbols illustrated in waveform 1202 representing the codeelements +1, +1, −1. The vertical dashed lines indicate the boundariesbetween separate code elements. The second waveform 1204 is illustrativeof a 5-level spreading symbol having the levels 0, +1, +2, +1, 0, −1,−2, −1, 0 for each spreading symbol. The code element assignments areidentical with those in 1202. The third waveform 1206 in FIG. 12represents a time multiplexed version of the second spreading symbolwaveform 1204. In the third waveform 1206 the first 2 code elements areshown as tertiary waveforms and are representative of the {+1, 0, −1}components in waveform 1202. The third code element in the thirdwaveform 1206 is representative of the outer levels of waveform 1204 at{+2, −2} but are transmitted after the first 2 code elements in thethird code element position and with a -1 code element assignment. Thefourth waveform 1208 in FIG. 12 is a replica based on the timemultiplexing of two Binary Offset Carrier signals, BOC(n,m) andBOC(k,l). The first 2 code elements are illustrated with a BOC(1,1)spreading symbol whilst the subsequent two code elements are illustratedwith a BOC(2,2) spreading symbol. The code assignments for code elements3 and 4 are −1 and +1 respectively. The code element duration is not thesame for each component in waveform 1208, at a rate of m×1.023 MHz and1×1.023 MHz whilst the sub-carrier components are at different offsetsfrom the carrier signal of n×1.023 MHz and k×1.023 MHz respectively. Anexemplary replica signal is formed with these parts occupying differentnon-overlapping time segments of the transmitted waveform. The replicawaveform follows an identical format in one embodiment.

Alternative embodiments employ the same general receiver format of FIG.11, but split the components of the signal so that these are carried viaseparate connections to the correlator processor 1112, and thecorrelator bank 1118. In one embodiment, the replica signal componentsare generated continuously and are gated in time so that the replicasignal generator 1116 only has signal outputs at the times correspondingthose that are appropriate for each component. These signals may bebinary, tertiary or have some other number of amplitude levels dependingupon the complexity of the transmitted signal format. The additionalprocessing step in the signal generator converting the continuoussignals at the time of generation to the output format required uses atime gate that allows passage of the signal at the time when it isrequired and prevents passage to the output otherwise.

In an alternative embodiment, the signals may have the time gateremoved, so that the signal components are continuously available at theinput to the correlation processor. The performance of a receiver usingthe continuous replica versions of the composite signal may havesub-optimum performance but may offer savings in receiver complexity.

The above embodiments have been described with reference to the I and Qchannels having the same chipping rates. However, embodiments are notlimited to such arrangements. Embodiments can be realised in whichdifferent chipping rates are used.

Although embodiments of the present invention have been described withreference to the L1 and L2 frequencies, embodiments are not limited tosuch arrangements. Embodiments can be realised in which otherfrequencies or frequency bands can be used according to the requirementsof the system using the invention. For example, the lower L band (ie E5aand E5b), the middle (ie E6) and upper L-band (ie E2-L1-E1) can alsobenefit from embodiments of the present invention. It will beappreciated that such embodiments may use signals having at least threecomponents rather than the two components described above.

Furthermore, embodiments of the present invention have been describedwith reference to standard BOC. However, one skilled in the artappreciated that embodiments can also be realised using Alternative BOC.

Still further, it will be appreciated that embodiments can be realisedin which the number of half cycles of a subcarrier per chip of a codecan be at least one of odd, even, an integer multiple or a non-integermultiple of the chip, that is, there is a rational number relationshipbetween the number of subcarrier half cycles and the chip duration.

Embodiments of the present invention described above have focused on thetransmission side of the invention, that is, upon the generation,modulation and transmission of signals such as, for example, spreadingsymbol modulation waveforms, composite signals, composite BOC signals,and ranging codes combined with a subcarrier or subcarriers and thelike. However, one skilled in the art appreciates that a conversesystem, method, apparatus and receiver are required to receive andprocess the signals. Once one skilled in the art has designed a systemfor generating and transmitting such signals, designing an appropriatereceiver is merely the converse of the transmit operations. Therefore,embodiments of the present invention also relate to systems, methods,apparatuses and receivers for processing signals such as those describedabove.

Although in the above mathematics relating to the above embodiments thesuperscripts “sin” and “cos” have been expressly used in some instancessuch as, for example, equations (3) and (3-1), it will be appreciated bythose skilled in the art that they are equally applicable to those termsthat do not expressly use them. It will also be appreciated thatembodiments can be realised in which the “sin” and “cos” superscriptsinterchanged.

The above embodiments have been described with reference to additivecombining of the BOC components. Embodiments are not limited to sucharrangements. Embodiments can be realised in which some other form ofcombining is used. For example, multiplicative combining can be used asan alternative. A further alternative to additive or multiplicativecombining might be an output from a logical network that processes anumber of BOC inputs to produce a composite output, which can be abinary or multi-level output.

Although the above embodiments have been described with reference to theoutput of at least one of the α and β generators being a squarewaveform, embodiments are not limited thereto. For example, the βgenerator can be formed by the combination of spreading code generator Ain combination with at least one further spreading code generator C.

The above embodiments have been described with to equal length spreadingcodes. However, embodiments are not limited thereto. For example,embodiments can be realised in which one of the spreading codegenerators has a period that is a multiple or sub-multiple of thespreading code period of another spreading code generator. Furthermore,embodiments can be realised in which the lengths of the spreading codesequences do not have a rational number relationship. For example, thelengths of the spreading code sequences may be prime numbers, productsof prime numbers or multiples of either.

It will be appreciated that the above embodiments have been describedwithout expressing the phase relationships between the spreading symbolmodulation waveforms. Embodiments can be realised in which, in anexemplary case in which there are two spreading symbol modulationsforming to composite BOC waveform (CBOC), the two spreading symbolwaveforms have a quadrature phase relationship or some other “out ofphase” phase relationship.

The invention claimed is:
 1. A receiver for receiving and processing anavigation signal comprising a ranging code modulated by a spreadingwaveform; said spreading waveform comprising at least a first portionand at least a second portion; said first portion comprising an additivecombination of first and second respective portions of first and secondBinary Offset Carrier (BOC) signals, having respective complexspectrums, with respective power spectral densities, said additivecombination exhibiting a first composite power spectral density having across spectral term with a first phase assignment; said second portioncomprising an additive combination of first and second respectiveportions of the first and second BOC signals, having respective complexspectrums, with respective power spectral densities, said additivecombination exhibiting a second composite power spectral density havinga cross spectral term with a second phase assignment; said second phaseassignment being complementary to the first phase assignment; thereceiver comprising an antenna for receiving the navigation signal; anRF processor for processing the received navigation signal and producingdigitised received signal samples therefrom; and a signal replicagenerator adapted to output a replica signal produced from the outputsof at least one or more of a carrier replica generator, a ranging codegenerator and a spreading waveform replica generator; and a correlationprocessor for correlating the replica signal and the digitised receivedsignal samples; wherein the at least current respective portions of saidfirst and second BOC signals comprises a predetermined number of chipsof the first and second BOC signals.
 2. The receiver as claimed in claim1, wherein the first respective portions of said first and second BOCsignals have said first phase state according to predeterminedtransitions of at least current respective portions of said first andsecond BOC signals.
 3. The receiver as claimed in claim 2 in which thepredetermined transitions of at least current respective portions offirst and second BOC signals are the same.
 4. The receiver as claimed inclaim 1 in which the first respective portions of said first and secondBOC signals comprises a predetermined number of chips of the first andsecond BOC signals spanning a period of a spreading waveform.
 5. Thereceiver as claimed in claim 1 in which the first and second BOC signalscomprise at least three signals.
 6. A non-transitory machine-readablestorage storing a program comprising executable instructions arranged,when executed, to implement a receiver as claimed in claim
 1. 7. Areceiver for processing a navigation signal comprising a carriermodulated by a ranging code combined with a Composite Binary OffsetCarrier (CBOC) waveform; the CBOC waveform having a predetermined powerspectral density comprising reduced cross spectral terms of the powerspectral densities of first and second Binary Offset Carrier (BOC)waveforms averaged over at least two predetermined time intervals; thestates of the first and second BOC signals, over a subsequentpredetermined time interval of the at least two predetermined timeintervals, being arranged to be complementary to the states of the firstand second BOC signals over a current predetermined time interval of theat least two predetermined time intervals; the receiver comprising an RFprocessor adapted to process the navigation signal to recover theranging signal; and a correlator to process the recovered rangingsignal; wherein at least first and second complementary power spectraldensities of the cross spectral terms of the first and second BOCwaveforms over the at least two predetermined time intervals aregenerated.
 8. The receiver as claimed in claim 7 in which thepredetermined power spectral density comprising at least reduced crossspectral terms of the power spectral densities of the first and secondBOC waveforms averaged over at least two predetermined time intervalscomprises substantially zero cross spectral terms of the power spectraldensities of the first and second BOC waveforms averaged over at leasttwo predetermined time intervals.
 9. A non-transitory machine-readablestorage storing a program comprising executable instructions arranged,when executed, to implement a receiver as claimed in claim
 7. 10. Amethod of processing a navigation signal, the navigation signalcomprising a ranging code modulated by a spreading waveform; saidspreading waveform comprising at least a first portion and at least asecond portion; said first portion comprising an additive combination offirst and second respective portions of first and second Binary OffsetCarrier (BOC) signals, having respective complex spectrums, withrespective power spectral densities, said additive combinationexhibiting a first composite power spectral density having a crossspectral term with a first phase assignment; said second portioncomprising an additive combination of first and second respectiveportions of the first and second BOC signals, having respective complexspectrums, with respective power spectral densities, said additivecombination exhibiting a second composite power spectral density havinga cross spectral term with a second phase assignment; said second phaseassignment being complementary to the first phase assignment; the methodcomprising the steps of receiving the navigation signal; anddemodulating the navigation signal to process the ranging code; whereinthe at least current respective portions of said first and second BOCsignals comprises a predetermined number of chips of the first andsecond BOC signals.
 11. A method as claimed in claim 10 wherein thefirst respective portions of said first and second BOC signals have saidfirst phase state according to predetermined transitions of at leastcurrent respective portions of said first and second BOC signals. 12.The method as claimed in claim 11 in which the predetermined transitionsof at least current respective portions of first and second BOC signalsare the same.
 13. The method as claimed in claim 10 in which the firstrespective portions of said first and second BOC signals comprises apredetermined number of chips of the first and second BOC signalsspanning a period of a spreading waveform.
 14. The method as claimed inclaim 10 in which the first and second BOC signals comprise at leastthree signals.
 15. A method for processing a navigation signalcomprising a carrier modulated by a ranging code combined with aComposite Binary Offset Carrier (CBOC) waveform; the CBOC waveformhaving a predetermined power spectral density comprising reduced crossspectral terms of the power spectral densities of first and secondBinary Offset Carrier (BOC) waveforms averaged over at least twopredetermined time intervals; the states of the first and second BOCsignals, over a subsequent predetermined time interval of the at leasttwo predetermined time intervals, being arranged to be complementary tothe states of the first and second BOC signals over a currentpredetermined time interval of the at least two predetermined timeintervals; the method comprising processing the navigation signal torecover the ranging signal; and correlating the recovered ranging signalwith a replica ranging signal; wherein at least first and secondcomplementary power spectral densities of the cross spectral terms ofthe first and second BOC waveforms over the at least two predeterminedtime intervals are generated.
 16. The method as claimed in claim 15 inwhich the predetermined power spectral density comprising at leastreduced cross spectral terms of the power spectral densities of thefirst and second BOC waveforms averaged over at least two predeterminedtime intervals comprises substantially zero cross spectral terms of thepower spectral densities of the first and second BOC waveforms averagedover at least two predetermined time intervals.
 17. A non-transitorymachine-readable storage storing a program comprising executableinstructions arranged, when executed, to implement a method as claimedin claim 15.